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How It Works
Manning's equation V = (1/n)Rh2/3S1/2 estimates the average velocity of open-channel flow from three inputs: the Manning roughness coefficient (n), the hydraulic radius (Rh), and the energy slope (S). It is the most widely used formula in hydraulic engineering for designing channels, culverts, and storm drains.
Example Problem
A concrete-lined channel (n = 0.013) has a hydraulic radius of 0.5 m and a slope of 0.002. What is the flow velocity?
- V = (1/0.013) × 0.52/3 × 0.0021/2
- V = 76.92 × 0.63 × 0.0447
- V ≈ 2.17 m/s
Frequently Asked Questions
What is Manning's roughness coefficient?
A dimensionless value representing channel surface friction. Finished concrete is about 0.012, earth channels 0.022, and natural rocky streams around 0.040. Lower n means a smoother surface and higher velocity.
Does Manning's equation work for pipes?
Yes, for gravity-flow pipes (not pressurized). For a full circular pipe of diameter D, the hydraulic radius is D/4. This calculator uses SI units (k = 1.0); for US customary units, multiply by 1.49.
What slope do I need for a 1 m/s flow in a concrete channel?
Rearranging for S: with n = 0.013 and Rh = 0.3 m, you need S ≈ 0.0012 (about 0.12%). Steeper slopes or smoother surfaces increase velocity.
Related Calculators
- Hydraulic Radius Calculator — compute Rh and Froude number for channel analysis.
- Chezy Equation Calculator — the historical predecessor to Manning's equation.
- Gutter Design Calculator — applies Manning's equation to roadway gutters.
- French Drain Design Calculator — subsurface drainage that complements open-channel flow.
- Continuity Equation Calculator — relate velocity, area, and discharge in channels.
- Length Unit Converter — convert channel dimensions between feet, meters, and other units.